How does electricity propagate in a conductor? On a systems level, I understand that as electrons are pushed into a wire, there is a net field and a net electron velocity.  And I've read that the net electron drift is slow.  But electricity travels through the wire, essentially at c, and I want to understand that mechanism.  My apologies if my question is poorly stated, I know bare bones undergraduate quantum theory circa 1990s but it doesn't explain the motion of electricity in detail.
Here's my conception, I'm hoping someone will fill in the holes, ha ha.
An electron moves into the wire.  It's got a kinetic energy.  After travelling a short distance, it spontaneously emits a photon, which hits another electron in a valence shell.  That electron then presumably does the same.
If this conception is simply wrong, please enlighten me.
The questions that arise:


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*Presumably at this level, electrons are acting more like waves and less like particles, but is there any classical component in the picture, ie are electrons coming in imparting other electrons with kinetic energy through repulsion, or does it not work that way?

*If electrons momentarily have energy, then pass it on by a photon, what determines when that photon is emitted, and what frequency it will be?  I assume that electrons in this cloud are not limited by any kind of exclusion principal, and that any frequencies are possible?

*Why should a photon emitted by an electron be in the direction of travel?  Conservation of momentum tells me that if an electron is moving, the photon should be emitted in that direction, slowing the electron, but could an electron emit a photon in the opposite direction?  If it did, I assume it would somehow have had to absorb energy from elsewhere? That sounds possible by analogy with quantum tunneling.

*What is the mechanism by which electrons propagating increase the temperature of the material?  Are they transmitting energy to the electrons in the valence shell, which tug at the nucleus, do some photons hit the nuclei directly, or is there some other way? 

*Presumably, electricity travels slower than light, because there is some time in each exchange, and some time when electrons are moving at sublight speeds before emitting a photon.  By how much is this slower than light, and what is the speed of each interaction?
 A: I will try to adress the misunderstandings first, then answer the question.
Particle exchange force model is not causal
There is a flaw in your thinking, in that you are formulating the electromagnetic interaction in terms of photon emission and absorption and at the same time telling a story forward in time. These two ideas are both ok separately, but not together.
The particle emission/absorption picture is not a causal picture--- it requires that the particles go back and forth in time--- so you can't use causal language, like an electron emits a photon which kicks an electron etc. That's part of the story, but another part of the story is: an electron emits a photons which had already kicked an electron earlier, which emitted a different photon earlier than the first, etc, etc. If you go to a unitary Hamitonian causal picture, you renounce the idea that the field is due to particle emission and absorption (I only said unitary for a technical reason: it is conceivable somebody could make a nonunitary Hamiltonian formulation with unphysical photon polarizations which contain the Coulomb force, but then these unphysical photons would only be intermediate states, since the physical photons are not responsible for the Coulomb interaction anyway).
The acausality in the Feynman description is not a problem with consistency, because there are causal formulations of QED, one of which is Dirac's. Here the electrostatic repulsion is not due to photon exchange, but is instantaneous action-at-a-distance, while photons travel with only the physical transverse polarization. In Feynman's particle push picture, the electrostatic interaction is due to unphysically polarized photons travelling much faster than the speed of light, and these photons just are not present in Dirac's equivalent formulation.
Anyway, the best way to understand electron motion is using the classical electric and magnetic fields produced by the electrons.
It's not the electrons pushing
The electrons in a wire are not pushed by other electrons. They are pushed by the external voltage applied to the wire. The voltage is a real thing, it is a material field, it has a source somewhere at the power plant, and the power plant transmits the power through electric and magnetic fields, not by electron pushes.
The electron repulsion in a metal is strongly screened, meaning that an electron travelling along at a certain speed will not repel an electron 100 atomic radii away. In many cases, it will even attract that electron due to weak phonon exchange (this weak attraction gives superconductivity, and essentially all ordinary metals become superconducting at some low enough temperature).
You can completely neglect the interelectron repulsion for the problem of conduction, and just ask about external fields rearranging charges in the wire.
Fermi surface, not wire surface
The only electrons that carry current are those near the Fermi surface. The Fermi surface is in momentum space, it is not a surface in physical space. The electrons which carry the current are distributed everywhere throughtout the wire. But they all have nearly the same momentum magnitude (if the Fermi surface is spherical, which I will assume without comment in the remainder).
The behavior of a Fermi gas is neither like a particle nor a wave. It is not a wave, because the occupation number is 0 or 1, so that there is no coherent superposition of a large number of particles in the same state, but it is also not like a particle, because the particle is not allowed to have momentum states lower than the Fermi momentum, by Pauli exclusion. The particle is traveling through a fluid of identical particles that jam up all the states with momentum smaller than the Fermi momentum.
This strange new thing (new in the 1930s, at least), is the Fermi quasiparticle. It is the excitation of a cold quantum gas, and to picture it in some reasonable terms, you have to think of a single particle which is always required to move at faster than a certain speed, it cannot slow down below this speed, because all these states are already occupied, but its can vary its direction. It has an energy which is proportional to the difference in speed from the lower bound. This lower bound on the speed in the Fermi velocity, which in metals is the velocity of an electron with wavelength a few angstroms, which is about the orbital velocity in the Bohr model, or a few thousand meters per second.
The Fermi liquid model of dense metals is the correct model, and it supersedes all previous models. The speed of the current carrying electrons is this few thousand meters per second, but at longer distances, there are impurities and phonons which scatter the electrons, and this can reduce the propagation to a diffusion process. The electronic diffusion doesn't have a speed, because distance in diffusion is not propotional to time. So the only reasonable answer to the question "what is the speed of an electron in a metal?" is the Fermi velocity, although one must emphasize that an injected electron will not travel a macroscopic distance at this speed in a metal with impurities.
1.Presumably at this level, electrons are acting more like waves and less like particles, but is there any classical component in the picture, ie are electrons coming in imparting other electrons with kinetic energy through repulsion, or does it not work that way?
In order to using a time-ordered causal langauge (this does that, then this does that), you need electric and magnetic fields, not photons. The electrons are not what is coming into the wire to make it conduct, the thing that is coming in is an electric field.
When you switch on a light, you touch a high voltage metal to a neutral metal, instantly raising the voltage, and making an electric field along the metal. This field accelerates the electrons near the Fermi surface (not on the wire surface, those near the fermi momentum) to travel faster in the direction of (minus) the electric field E. It can only accelerate those electrons which can be sped up into new states, so it only speeds up electrons which are already running around at the Fermi velocity. These electrons keep moving until they build up enough charge on the surface of the metal to cancel out the electric field, and to bend the electric field direction to follow the wire wherever the wire curves. This causal propagation is Field-Electrons-Field, and the only electrons which serve to shunt the field are those which are building up charges on the surface of the wire (and the protons on the surface which also redirect the field where there needs to be positive charge)
When you apply a constant voltage, the electrons come to a steady state where they are carrying the current from the negative voltage to the positive voltage, making the voltage drops line up in space along the direction of the wire, no matter what the shape, and bouncing off impurities and phonons to dissipate the energy they get from the field into phonons (heat). The local electric field drives their motion, not their mutual repulsion. In that sense, it is not like water in a pipe. It is more like a collection of independent ball bearings pushed by a magnet, except that the ball bearings shunt the magnetic field to go along the direction of their motion.
2.If electrons momentarily have energy, then pass it on by a photon, what determines when that photon is emitted, and what frequency it will be? I assume that electrons in this cloud are not limited by any kind of exclusion principal, and that any frequencies are possible?
The electrons in the cloud are not only limited by exclusion, they are dominated by exclusion, this is the Fermi gas. It is not the electrons pushing other electrons, it is the field pushing the electrons. The photon particle-exchange picture is irrelevant to this, but if you insist on using it, then the photons are coming out of the wall socket, having followed the high-voltage wires from the power-plant in a back-and-forth zig-zag in time, and a negligible fraction of the photons are emitted by the conduction electrons, since all those photons are absorbed into phonons by the metal within a screening length.
The photons coming from the wall are bounced around by surface charges on the wire (static electrons and protons) so that they bounce around to follow the path of the wire in steady state.
3. Why should a photon emitted by an electron be in the direction of travel? Conservation of momentum tells me that if an electron is moving, the photon should be emitted in that direction, slowing the electron, but could an electron emit a photon in the opposite direction? If it did, I assume it would somehow have had to absorb energy from elsewhere? That sounds possible by analogy with quantum tunneling.
Photons are emitted in all directions, and back in time. It just is not useful to think of Feynman picture when you want to think causally.
4. What is the mechanism by which electrons propagating increase the temperature of the material? Are they transmitting energy to the electrons in the valence shell, which tug at the nucleus, do some photons hit the nuclei directly, or is there some other way?
So far, I have been treating the electrons as a gas of free particles. But you might be upset--- there are lots nuclei around! How can you treat them as a gas? Don't they bounce off the nuclei?
The reason you can do this is that a quantum mechanical particle which is confined to a lattice, which has amplitudes to hop to neighboring points behaves exactly the same as a free particle obeying the Schrodinger equation (at least at long distances). It does not dissipate at all, it just travels along obeying a discrete version of the Schrodinger equation with a different mass, determined by the hopping amplitudes.
In Solid State physics, this type of picture called the "tight binding model", but it is really more universal than this. In any potential, the electrons make bands, and the bands fill up to the Fermi surface. But the picture is not different from a free gas of particles, except for losing rotational symmetry.
If the lattice were perfect, this picture would be exact, and the metal would not have any dissipation losses at all. But at finite temperature there are phonons, defects, and a thermal skin of electrons already excited at a little more energy than the Fermi surface. The phonons, defects, and thermal electrons can scatter the conducting electrons inelastically, and this is the mechanism of energy loss. The electrons can also emit phonons spontaneously, if their energy is far enough above the Fermi surface so that they are no longer stable. All of these effects tend to vanish at zero temperature (with the exception of defects, which can be frozen in, but then the defects become elastic). But at cold enough temperatures, you don't go to zero conduxctivity smoothly. Instead, you tend to have a phase transition to a superconducting state.
5. Presumably, electricity travels slower than light, because there is some time in each exchange, and some time when electrons are moving at sublight speeds before emitting a photon. By how much is this slower than light, and what is the speed of each interaction?
This is again confusing Feynman description with a causal description. But I did this experiment as an undergraduate, and along a good coaxial cable, the speed was 2/3 the speed of light. I assume that if you use an ordinary wire in a coil on the floor, its going to be significantly slower, perhaps only 1% of the speed of light, because it requires more finnagling of surface charges for the wire to set up the field to follow it curves.
A: 
And I've read that the net electron drift is slow. But electricity travels through the wire, essentially at c, and I want to understand that mechanism.

I'm just going to answer this part in a handwavy way.  All the electrons in the wire are repelling each other, right?  They want to be as far apart as possible.  If they are stable and motionless, and then you push on one of them, it will exert a force on its neighbors, which causes them to move a little farther away.  Their movement exerts a force on their neighbors, etc.  A wave travels through all the electrons, though the individual electrons themselves don't move very far.  This wave is what carries energy, not the electrons themselves.  When you flip a light switch, the electrons don't have to travel all the way from the switch to the light.  The electron fluid moves very slowly, but the wave travels through the electron fluid and hits the light bulb at close to c.  The wave causes the electrons that were already in the light bulb to start moving and heating it up.
Imagine a long pipe full of water with pistons at each end.  When you push your piston inwards a little, the water in front of is is compressed.  This then pushes on the water next to it, which pushes on the water next to it, etc. until the wave reaches the other end, at which point the other piston pops out a little.  The water molecules themselves only move a little bit in one direction, and then stop.  The pressure wave travels at the speed of sound through the pipe and does work at the other end.


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*THE "ELECTRICITY" INSIDE OF WIRES MOVES AT THE SPEED OF LIGHT? Wrong.

*Acoustics and Vibration Animations - Dan Russell

4.What is the mechanism by which electrons propagating increase the temperature of the material?

I don't pretend to understand this, but this is caused by "destructive interference of free electron waves on non-correlating potentials of ions".  The thermal motion of ions in the metal scatters electrons, causing resistance, which causes the thermal motion of ions...


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*Wikipedia:Causes of resistance (archived version)

*Wikipedia:Causes of conductivity
A: My simple view in layman's terms.  Electricity is like water flowing in a river. The river are the wires and the electrons are the logs in the river, copper is full of logs by the way. So the photons are like the water moving very quickly propelled by high to low pressure (volts). As the water in the river passes the logs (electrons) it moves them slowly along following the flow of the water. The water moves at nearly the speed of light because they are photons. The logs slow them a little bit. The logs move very slowly. The log momentum is what we recognize as induction. Dc will induce more log momentum (induction) than ac because the water continues in the same direction. A large inductor will act as a smoothing effect for Dc as the logs momentum adds or subtracts to variations.  Ac always see a large inductor as restriction because of the logs constantly changing direction and resisting all motions as all mass does. Nearly every conductor has some induction. The logs(electrons) have momentum and the water(photons) do not. This is why induction currents act exactly like logs with momentum. When the water is suddenly stopped the logs momentum or induction can keep the pressure building in the water and create a secondary pressure and flow that is independent of the source. So during the bemf event the logs can force the stopped water to continue, since there is no river opening left (because the switch is off). so as soon as enough pressure is built from the logs momentum they can break out and release the water (photons) into a new river just like a levy break. Long rivers have more logs and induction than short ones this is the reason we make coils to increase induction measured in henries . The logs momentum can be stored in spinning chambers in large warehouses along the river. These are the transformer and iron cores inside of so many coils made of laminated iron. It is essential to keep them in chambers laminations or powdered type to keep the log momentum storage to a maximum. So magnetic fields are spinning logs with momentum. The very reason the swirling iron core of the earth is a magnet. Its a big transformer core ware house of spinning logs. As the frequencies begin to get real high the water can evaporate and leave the river. We recognize this as RF energy. Which can travel loss-less and at full speed of C there is no logs in space however they spread in every direction because they left the river.
In some rivers the logs can be frozen in place and allow the water to travel loss-less this is superconductors no log motion due to extreme lock down of the logs. Batteries are like water pumps resistors are sandbars and amps measure the water plus log motion. we do not have a meter than can separate the 2 kinds of flow this is the large confusion we all have with cold electricity. If you can get photon flow only it will be nearly loss-less and run cool and much more efficient like the tesla radiant energy transfer towers. At very high voltage, high frequency and rapid pulses the logs do not have the time to get any momentum and the efficiency of wires can increase. A spark gap would be a river blowing a levy to get to another river. This is the reason a spark gap can create efficient operation again it creates high frequency as the levy breaks and holds at an extremely rapid rate. Alot free energy devices seem to keep coming back to spark gaps or high frequencies. A magnet is a special ware house where the logs have been locked into a spin by design if forced to stop they will spin back up again. This is the reason we can never extract the energy from the ware house of spinning logs in a magnet because the magnet will steal and  demand energy back to bring the logs back up to a spin again due to the locked in arrangement of the atoms. If brought up to Neil temperature the magnet will loose its locked in log spin design. A capacitor is a rubber membrane set across the river like a dam. The alternating water motion can be transferred pretty good as the rubber stretches but the direct flows will be blocked just like a wall. The rubber membrane can store energy as it stretches as direct pressure on the water is maintained if the river is switched off. Just like a bladder tank in a standard house with a water well. Size of tank is measured in mfd and pressure tank rating is in volts. The waves in the river can cancel or add to each other with great complexities.  There can be check valves (diodes in rivers to set up one way travel of water and logs) As the logs bump along with each other or on sandbars they generate heat this is resistance. A light bulb would be a restriction in the river like a small pipe in a dam the water can evaporate and leave the river as soon as temperature of the restriction (filament) reaches evaporation energy levels. Bottom line is there are 2 types of flows (photon) very fast with no momentum near speed of light. The other (elctron) very slow with but with momentum and ability to be stored and transferred thru transformer cores to other rivers. The photon type can evaporate and leave the river while the other type stays with the conductor. except in some situations inside of picture tubes where they can be shot onto the screen. CRT. Cold electricity = photon flow only inside the conductor. Radiant energy = evaporation of photon flow from the wires into free space.  Each type of current can induce the other. 
